come out vs come forth

come out and come forth both are verbs.

Word	Noun	Adjective	Verb	Adverb
come out	No	No	Yes	No
come forth	No	No	Yes	No

As verbs, come out and come forth are synonyms defined as:

Other synonyms of come out include egress, emerge, go forth, issue.

As verbs, come forth is a hypernym of come out; that is, come forth is a word with a broader meaning than come out:

Other hypernyms of come out include come out, egress, emerge, go forth, issue.

come out (verb)	come forth (verb)
appear or become visible; make a showing	come out of
be issued or published	happen or occur as a result of something
break out
come out of
take a place in a competition; often followed by an ordinal
be made known; be disclosed or revealed
to state openly and publicly one's homosexuality
bulge outward
make oneself visible; take action
drop out
result or end